My perspective on SJ is that their core is aging, and the prospect cupboards aren't as full as other teams. Karlsson signing there doesn't change their age.
Karlsson controls where he wants to go, and he might indeed like it there, and perhaps wants to sign in SJS for a short-term extension, but how will that team look in the latter part of a long-term extension?
Remember:
SJ = No 2019 1st , no 2020 1st. It is conceivable that there would be no 2021 1st as well, if he does indeed re-sign (and they make the cup final, otherwise no 2nd).
Player ages next year: Thornton (40), Pavelski (35), Burns (34), Braun (32), Vlasic (32), Couture (30), etc. Still some juice left for next year, maybe another year after that, but many of these players (the core) will be on the decline.
If he signs in SJ it is for a short-term extension IMO, but I still think even if he likes it there, he is much more likely to sign elsewhere after this year.